Control algorithms have been proposed based on knowledge related to nature-inspired mechanisms, including those based on the behavior of living beings. This paper presents a review focused on major breakthroughs carried out in the scope of applied control inspired by the gravitational attraction between bodies. A control approach focused on Artificial Potential Fields was identified, as well as four optimization metaheuristics: Gravitational Search Algorithm, Black-Hole algorithm, Multi-Verse Optimizer, and Galactic Swarm Optimization. A thorough analysis of ninety-one relevant papers was carried out to highlight their performance and to identify the gravitational and attraction foundations, as well as the universe laws supporting them. Included are their standard formulations, as well as their improved, modified, hybrid, cascade, fuzzy, chaotic and adaptive versions. Moreover, this review also deeply delves into the impact of universe-inspired algorithms on control problems of dynamic systems, providing an extensive list of control-related applications, and their inherent advantages and limitations. Strong evidence suggests that gravitation-inspired and black-hole dynamic-driven algorithms can outperform other well-known algorithms in control engineering, even though they have not been designed according to realistic astrophysical phenomena and formulated according to astrophysics laws. Even so, they support future research directions towards the development of high-sophisticated control laws inspired by Newtonian/Einsteinian physics, such that effective control-astrophysics bridges can be established and applied in a wide range of applications.

In the field of transcutaneous functional electrical stimulation (FES), open-loop and closed-loop control strategies have been developed to restore functions of the lower limbs: walking, standing up, maintaining posture, and cycling. These strategies require sensors that provide feedback information on muscle activity or biomechanics of movement. Since muscle response induced by transcutaneous FES is nonlinear, time-varying, and dependent on muscle fatigue evolution, the choice of sensor type and control strategy becomes critical. The main objective of this review is to provide state-of-the-art, emerging, current, and previous solutions in terms of control strategies. Focus is given on transcutaneous FES systems for the lower limbs. Using Compendex and Inspec databases, a total of 135 review and conference articles were included in this review. Recent studies mainly use inertial sensors, although the use of electromyograms for lower limbs has become more frequent. Currently, several researchers are opting for nonlinear controllers to overcome the nonlinear and time-varying effects of FES. More development is needed in the field of systems using inertial sensors for nonlinear control. Further studies are needed to validate nonlinear control systems in patients with neuromuscular disorders.

This review shows the potential ground-breaking impact that mathematical tools may have in the analysis and the understanding of the HIV dynamics. In the first part, early diagnosis of immunological failure is inferred from the estimation of certain parameters of a mathematical model of the HIV infection dynamics. This method is supported by clinical research results from an original clinical trial: data just after 1 month following therapy initiation are used to carry out the model identification. The diagnosis is shown to be consistent with results from monitoring of the patients after 6 months. In the second part of this review, prospective research results are given for the design of individual anti-HIV treatments optimizing the recovery of the immune system and minimizing side effects. In this respect, two methods are discussed. The first one combines HIV population dynamics with pharmacokinetics and pharmacodynamics models to generate drug treatments using impulsive control systems. The second one is based on optimal control theory and uses a recently published differential equation to model the side effects produced by highly active antiretroviral therapy therapies. The main advantage of these revisited methods is that the drug treatment is computed directly in amounts of drugs, which is easier to interpret by physicians and patients.